Homework help_MEE 312 – Engineering Materials

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MEE 312 – Engineering Materials

Homework 7

Due Monday, April 3 in class

1)  Briefly (in a single phrase or short sentence) describe/define the following terms in your own words and, if relevant, include an example:

  1. Solid solution               f)     Hume-Rothery rules
  2. Phase               g)    Freezing range
  3. Gibbs phase rule               h)    Tie line
  4. Unlimited solubility               i)     Lever rule
  5. Limited solubility

2)  How does a binary phase diagram differ from a unary phase diagram?  When a binary phase diagram is referred to as “isomorphous,” what does that mean?

3)  In the context of a binary phase diagram, how does the composition of a phase differ from the amount of a phase?

4)  Based on the Hume-Rothery rules, which alloy would you expect to have unlimited solid solubility?  (Hint: Consult Appendices A and B in your textbook, and make sure you understand which of the H-R rules are violated for the alloys below with limited solubility.)

  1. Cu-Zn alloy
  2. Al-Cu alloy
  3. Mg-Zn alloy
  4. Au-Ag alloy

5)  Use the following phase diagram for a NiO-MgO ceramic to answer the following questions:

  1. This phase diagram is best classified as
    1. Unary and isomorphous
    2. Binary and isomorphous
    3. Binary and polymorphous
    4. Ternary and polymorphous
  1. The liquidus temperature for NiO-20% MgO is
    1. Lower than NiO-40% MgO
    2. Higher than NiO-40% MgO
    3. The same regardless of composition
    4. The same as the solidus temperature for NiO-20% MgO
  • Estimate the solidus temperature, liquidus temperature, and freezing range for a NiO-60% MgO alloy.
  1. The freezing range is largest for ______________, and smallest for _______________

and _________________.

  1. If we wanted to heat treat (anneal) a solid ingot of NiO-50% MgO alloy to enhance its ductility, we would need to do so below what temperature and why?
  2. Use the Gibbs phase rule to prove that there are two degrees of freedom in the regions of the phase diagram where only the liquid L or solid S phase is present, and one degree of freedom in the two-phase (L + S) region. Which form of the Gibbs phase rule will you use to prove this, and why?
  • For NiO-60% MgO, determine the phases present at each of the following temperatures:
    1. 2200 C
    2. 2500 C
    3. 2700 C

Then, at each temperature, estimate (i) the composition of each phase and (ii) the amount of each phase.

  • Describe the evolution of the composition of NiO-60% MgO as it is cooled from a molten liquid at 2700 C, through the two-phase region, to a solid ceramic at 2200 C.
  1. In general, what would you expect to happen to the mechanical properties (e.g., strength and ductility) of a NiO-MgO ceramic as you increase the mol % NiO?

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